TN SYLLAQBUS STD 12

2.  An electrical conductor has a large number of
mobile charges which are free to move in the
material.
 In a metallic conductor, these mobile charges
are free electrons which are not bound to any
atom and therefore are free to move on the
surface of the conductor.
 When there is no external electric field, the free
electrons are in continuous random motion in all
directions

3.  As a result, there is no net motion of electrons
along any particular direction which implies that
the conductor is in electrostatic equilibrium.
 Thus at electrostatic equilibrium, there is no net
current in the conductor. A conductor at
electrostatic equilibrium has the following
properties.

4.  (i) The electric field is zero everywhere inside
the conductor. This is true regardless of
whether the conductor is solid or hollow.
 Suppose the electric field is not zero inside the
metal, then there will be a force on the mobile
charge carriers due to this electric field.
 As a result, there will be a net motion of the
mobile charges, which contradicts the
conductors being in electrostatic equilibrium.
 Thus the electric field is zero everywhere inside
the conductor.

6.  Before applying the external electric field, the
free electrons in the conductor are uniformly
distributed in the conductor.
 When an electric field is applied, the free
electrons accelerate to the left causing the left
plate to be negatively charged and the right
plate to be positively charged
 Due to this realignment of free electrons, there
will be an internal electric field created inside
the conductor which increases until it nullifies
the external electric field.

7.  Once the external electric field is nullified the
conductor is said to be in electrostatic
equilibrium.
 The time taken by a conductor to reach
electrostatic equilibrium is in the order of 10-
16s, which can be taken as almost
instantaneous.

8.  (ii) There is no net charge inside the
conductors. The charges must reside only on
the surface of the conductors
 Consider an arbitrarily shaped conductor
 A Gaussian surface is drawn inside the conductor
such that it is very close to the surface of the
conductor.
 Since the electric field is zero everywhere inside
the conductor, the net electric flux is also zero over
this Gaussian surface.
 From Gauss’s law, this implies that there is no net
charge inside the conductor.
 Even if some charge is introduced inside the
conductor, it immediately reaches the surface of
the conductor.

10.  (iii) The electric field outside the conductor is
perpendicular to the surface of the conductor
and has a magnitude of σ /ε0 where σ is the
surface charge density at that point.
 If the electric field has components parallel to
the surface of the conductor, then free
electrons on the surface of the conductor would
experience acceleration
 This means that the conductor is not in
equilibrium. Therefore at electrostatic
equilibrium, the electric field must be
perpendicular to the surface of the conductor

13.  We now prove that the electric field has
magnitudeσ /ε0 just outside the conductor’s
surface
 Consider a small cylindrical Gaussian surface
One half of this cylinder is embedded inside the
conductor.
 Since electric field is normal to the surface of
the conductor, the curved part of the cylinder
has zero electric flux.
 Also inside the conductor, the electric field is
zero. Hence the bottom flat part of the
Gaussian surface has no electric flux

14. 
 Therefore the top flat surface alone contributes
to the electric flux. The electric field is parallel
to the area vector and the total charge inside
the surface is σA
 Here represents n the unit vector outward
normal to the surface of the conductor.
Suppose σ < 0, then electric field points inward
perpendicular to the surface.

16.  (iv) The electrostatic potential has the same
value on the surface and inside of the
conductor.
 We know that the conductor has no parallel electric
component on the surface which means that
charges can be moved on the surface without
doing any work.
 This is possible only if the electrostatic potential is
constant at all points on the surface and there is no
potential difference between any two points on the
surface.
 Since the electric field is zero inside the conductor,
the potential is the same as the surface of the
conductor.
 Thus at electrostatic equilibrium, the conductor is
always at equipotential.

17.  Consider a cavity inside the conductor
 Whatever the charges at the surfaces and
whatever the electrical disturbances outside,
the electric field inside the cavity is zero.
 A sensitive electrical instrument which is to be
protected from external electrical disturbance is
kept inside this cavity. This is called
electrostatic shielding

18.  Faraday cage is an instrument used to
demonstrate this effect
 If an artificial lightning jolt is created outside, the
person inside is not affected
 During lightning accompanied by a thunderstorm, it
is always safer to sit inside a bus than in open
ground or under a tree.
 The metal body of the bus provides electrostatic
shielding, since the electric field inside is zero.
 During lightning, the charges flow through the
body of the conductor to the ground with no effect
on the person inside that bus